Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23765232 | C2 | semidirect |
| 2. #23765219 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 5. #23761356 | C2 | semidirect |
| 6. #23761319 | C2 | semidirect |
| 7. C79×D4⋊C16 | C2 | semidirect |
| 83. D316 | M32 | semidirect |
| 119. D4⋊C16 | D79 | semidirect |
| 121. C79 | #12063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765232 | 2 |
| #23765219 | 2 |
| C8×#11929609 | 2 |
| #23761463 | 2 |
| #23761356 | 2 |
| #23761319 | 2 |
| C79×D4⋊C16 | 2 |
| #12063 | 79 |